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Are only 2 bits of information transmitted in quantum teleportation?

Prompted by the recent success in Delft, I've been reading a number of papers and articles about quantum teleportation. I'm comfortable with my understanding of most aspects but haven't found much ...
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A foundational question about entanglement

The recent Nature article http://www.nature.com/news/data-teleportation-the-quantum-space-race-1.11958 prompts me to ask this question, which is of the same tenor as that asked at the recent Perimeter ...